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Transcript
Step Ahead Numbers the Mathematics Enrichment Program offered in connection with MATH 010, Queen's University, Fall 2007 Thank you for the opportunity to provide the enrichment program. We hope your students enjoyed it as much as we did. The topics we covered with your students, including the activities used, are checked off below: TOPICS COVERED 1. Number Patterns and Explanations □ Examples of patterns in number sequences □ An exploration of infinite sets □ An introduction/review of the use of formulas in mathematics □ The distinction between the pattern rule and the resulting sequence 2. Growth Rates of Sequences □ Why different sequences grow at very different rates □ Measuring growth rates (using a story about magic boxes) □ Exponential notation for powers higher than squares 3. Division □ Divisibility tricks (by 2, 3, 4, 5 & 9) □ Prime number factorization □ Estimating the digits in 213466917-1, the largest known prime number □ Applications to greatest common factor and least common multiple 4. Fractions □ Fractions that correspond to both terminating and repeating decimals □ Rational and irrational numbers □ √2 as an irrational number □ Decimal expressions and the number line ENRICHMENT ACTIVITIES □ E.A. 1.1 – Recognizing Patterns □ E.A. 1.2 – The Infinite Motel □ E.A. 1.3 – Pattern Rules Producing the Same Sequence □ E.A. 1.4 – The Role of Proof □ E.A. 1.5 – Patterns Produced Geometrically □ E.A. 2.1 – Measuring the Growth Rate of a Sequence □ E.A. 2.2 – The Poor Soldier and the King □ E.A. 3.1 – Prime Number Factors □ E.A. 3.2 – What Prime Factors Tell □ □ □ □ □ □ □ □ □ □ You E.A. 3.3 – Number Magic E.A. 3.4 – How Many Primes Are There? E.A. 3.5 – Greatest Common Factor E.A. 3.6 – Least Common Multiple P.S. 3.7 – Practice Using Prime Factorizations E.A. 4.1 – Fractions and Decimals E.A. 4.2 – Terminating or Repeating? P.S. 4.3 – Practice with Fractions and Decimals E.A. 4.4 – Rational and Irrational Numbers E.A. 4.5 – The Difference Between 0.99999… and 1 continued on back 5. Remainders □ Simple modular arithmetic (arithmetic that focuses on the remainders left after division by a prime number) □ An explanation of the trick for divisibility by 3, using modular arithmetic 6. Counting □ Counting and organizing large collections □ Interpreting a counting problem and finding the appropriate mathematics to model it 7. Probability □ Introduction to probability as a problem of counting a set of equally likely outcomes □ Calculating probabilities □ The concept of risk (a concept combining probability and cost) and risk calculations Other □ □ □ □ □ E.A. 5.1 – Some Strange Division □ □ □ □ Problems E.A. 5.2 – Jelly Beans E.A. 5.3 - Multiplication P.S. 5.4 – Apples and Oranges E.A. 5.5 - Leftovers □ E.A. 6.1 – Finding a System □ P.S. 6.2 – Counting Practice □ E.A. 6.3 – Coins and Dice □ E.A. 7.1 – Equally Likely □ □ □ □ □ □ □ □ Outcomes P.S. 7.2 – Probability Practice E.A. 7.3 – Should we be Surprised? P.S. 7.4 – More Practice E.A. 7.5 – What is the Risk?